Whether the force for the supported height adjustment is due to a motor, a spring, gravity or is generated manually, it is desirable, that the rods of the headrests can be vertically moved in their holders in the Z-direction without an application of excessive effort. This requires an exactly parallel alignment of the said rods and their shells within the planes YZ and YX and calls for a predetermined separating distance of the rods and shells. Due to manufacturing procedures, it cannot entirely be avoided, that the rods and their shells deviate from ideal alignment, which engenders a situation wherein the effort necessary for vertical movement of the headrest becomes greater. This causes a manual height adjustment to be more difficult and leads to difficulties for automatic operation.